This Devilishly Hard Logic Puzzle Will Save Your Life

This week’s puzzle is difficult. Not because it has an exceedingly complicated solution, but because the idea that underlies it is deep and ingenious. I only know of one method to solve it, but I’m curious whether alternative approaches exist. Feel free to spitball half-baked ideas in the comments. You might find working together on solutions an enriching experience. But also, your life depends on it.

Did you miss last week’s puzzle? Check it out here, and find its solution at the bottom of today’s article. Be careful not to read too far ahead if you haven’t solved last week’s yet!

Puzzle #32: Forehead or Dead

A madman is holding you and nine strangers captive. He subjects you to a twisted mind game to earn your freedom. He has a stack of cards with the numbers 0 through 9 printed on them. He tapes a card to every person’s forehead so everyone can see everybody else’s card but not their own. Assigned numbers may repeat (e.g. eight people could get 7s while the other two get 0s or any other combination). After everyone has had time to observe everyone else’s numbers, your captor counts down and you all must shout a number at the same time. If at least one person guesses the correct number on their forehead, then you all go free. Otherwise you’ll be condemned to solve riddles in his basement forever.

As a madman with a passion for problem-solving, he allows the group to confer before he distributes the cards. Once cards are revealed no communication (including nonverbal) is allowed other than shouting a number on cue. The villain may listen in on the group strategy and adapt his choices accordingly! Devise a strategy that guarantees your freedom.

I recommend solving this for two or three people first and then trying to generalize the approach. Note that in the two person case, the cards only say 0 or 1, and in the three person version they say 0, 1, or 2.

I’ll be back next Monday with the solution. I hope it’s not too late for you.

Do you know a cool puzzle that you think should be featured here? Message me on X @JackPMurtagh or email me at gizmodopuzzle@gmail.com

Solution to puzzle #31: HIPE Me Up

Did last week’s word puzzles live up to the hype? Shout-out to Skylar Ruprecht for proposing a really good original HIPE in the comments: EAUC. Try it out. Meanwhile, here are the answers to last week’s HIPES:

• BV — this one was OBVIOUS.
• WKW – AWKWARD
• ONIG – TONIGHT
• SPB – RASPBERRY
• RAOR – EXTRAORDINARY
• HQ – EARTHQUAKE
• TANTAN – INSTANTANEOUS

• PTC – BANKRUPTCY
• GUAG – LANGUAGE